LMFDB - Embedded newform 2646.2.l.b.521.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(521,2646)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2646.521");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.l (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 6x^{14} + 9x^{12} + 54x^{10} - 288x^{8} + 486x^{6} + 729x^{4} - 4374x^{2} + 6561 $ x^16 - 6x^14 + 9x^12 + 54x^10 - 288x^8 + 486x^6 + 729x^4 - 4374*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			521.3
Root			$-1.40917 + 1.00709i$ of defining polynomial
Character	$\chi$	$=$	2646.521
Dual form			2646.2.l.b.1097.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +1.00000i q^{8} +(-2.03460 - 1.17468i) q^{10} +(-4.91614 + 2.83834i) q^{11} +(-1.48943 + 0.859925i) q^{13} +1.00000 q^{16} +(0.884414 - 1.53185i) q^{17} +(0.986680 - 0.569660i) q^{19} +(-1.17468 + 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +(-3.18272 - 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} +(0.859925 + 1.48943i) q^{26} +(-3.59886 - 2.07781i) q^{29} +8.37019i q^{31} -1.00000i q^{32} +(-1.53185 - 0.884414i) q^{34} +(4.59886 + 7.96547i) q^{37} +(-0.569660 - 0.986680i) q^{38} +(2.03460 + 1.17468i) q^{40} +(3.99709 + 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(4.91614 - 2.83834i) q^{44} +(-1.83755 + 3.18272i) q^{46} -11.8099 q^{47} +(-0.449885 + 0.259741i) q^{50} +(1.48943 - 0.859925i) q^{52} +13.3365i q^{55} +(-2.07781 + 3.59886i) q^{58} -2.22966 q^{59} +8.99970i q^{61} +8.37019 q^{62} -1.00000 q^{64} +4.04054i q^{65} +10.8712 q^{67} +(-0.884414 + 1.53185i) q^{68} -4.52106i q^{71} +(4.62660 + 2.67117i) q^{73} +(7.96547 - 4.59886i) q^{74} +(-0.986680 + 0.569660i) q^{76} -13.0284 q^{79} +(1.17468 - 2.03460i) q^{80} +(6.92317 - 3.99709i) q^{82} +(-6.27298 + 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(-3.04933 - 1.76053i) q^{86} +(-2.83834 - 4.91614i) q^{88} +(0.580529 + 1.00551i) q^{89} +(3.18272 + 1.83755i) q^{92} +11.8099i q^{94} -2.67667i q^{95} +(3.97536 + 2.29517i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{4}+O(q^{10}) $ 16 * q - 16 * q^4	$ 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) $ 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	1.17468	−	2.03460i	0.525332	−	0.909902i	−0.474232	−	0.880400i	$-0.657274\pi$
$5$	1.17468	−	2.03460i	0.525332	−	0.909902i	0.999565	−	0.0295026i	$-0.00939234\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−2.03460	−	1.17468i	−0.643398	−	0.371466i
$11$	−4.91614	+	2.83834i	−1.48227	+	0.855790i	−0.999798	−	0.0201197i	$-0.993595\pi$
$11$	−4.91614	+	2.83834i	−1.48227	+	0.855790i	−0.482475	+	0.875910i	$0.660262\pi$
$12$		0			0
$13$	−1.48943	+	0.859925i	−0.413094	+	0.238500i	−0.692118	−	0.721784i	$-0.743322\pi$
$13$	−1.48943	+	0.859925i	−0.413094	+	0.238500i	0.279024	+	0.960284i	$0.409989\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	0.884414	−	1.53185i	0.214502	−	0.371528i	−0.738616	−	0.674126i	$-0.764520\pi$
$17$	0.884414	−	1.53185i	0.214502	−	0.371528i	0.953118	+	0.302598i	$0.0978538\pi$
$18$		0			0
$19$	0.986680	−	0.569660i	0.226360	−	0.130689i	−0.382532	−	0.923942i	$-0.624948\pi$
$19$	0.986680	−	0.569660i	0.226360	−	0.130689i	0.608892	+	0.793253i	$0.291614\pi$
$20$	−1.17468	+	2.03460i	−0.262666	+	0.454951i
$21$		0			0
$22$	2.83834	+	4.91614i	0.605135	+	1.04812i
$23$	−3.18272	−	1.83755i	−0.663644	−	0.383155i	0.130020	−	0.991511i	$-0.458496\pi$
$23$	−3.18272	−	1.83755i	−0.663644	−	0.383155i	−0.793664	+	0.608356i	$0.791829\pi$
$24$		0			0
$25$	−0.259741	−	0.449885i	−0.0519482	−	0.0899769i
$26$	0.859925	+	1.48943i	0.168645	+	0.292102i
$27$		0			0
$28$		0			0
$29$	−3.59886	−	2.07781i	−0.668292	−	0.385839i	0.127137	−	0.991885i	$-0.459421\pi$
$29$	−3.59886	−	2.07781i	−0.668292	−	0.385839i	−0.795429	+	0.606046i	$0.792755\pi$
$30$		0			0
$31$			8.37019i			1.50333i	0.659545	+	0.751665i	$0.270749\pi$
$31$			8.37019i			1.50333i	−0.659545	+	0.751665i	$0.729251\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$	−1.53185	−	0.884414i	−0.262710	−	0.151676i
$35$		0			0
$36$		0			0
$37$	4.59886	+	7.96547i	0.756049	+	1.30951i	0.944851	+	0.327500i	$0.106206\pi$
$37$	4.59886	+	7.96547i	0.756049	+	1.30951i	−0.188803	+	0.982015i	$0.560461\pi$
$38$	−0.569660	−	0.986680i	−0.0924111	−	0.160061i
$39$		0			0
$40$	2.03460	+	1.17468i	0.321699	+	0.185733i
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	0.988687	+	0.149993i	$0.0479251\pi$
$41$	3.99709	+	6.92317i	0.624241	+	1.08122i	−0.364446	+	0.931225i	$0.618742\pi$
$42$		0			0
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	−0.699991	−	0.714152i	$-0.746813\pi$
$43$	1.76053	−	3.04933i	0.268478	−	0.465018i	0.968469	+	0.249134i	$0.0801459\pi$
$44$	4.91614	−	2.83834i	0.741136	−	0.427895i
$45$		0			0
$46$	−1.83755	+	3.18272i	−0.270931	+	0.469267i
$47$	−11.8099			−1.72265			−0.861324	−	0.508055i	$-0.830365\pi$
$47$	−11.8099			−1.72265			−0.861324	+	0.508055i	$0.830365\pi$
$48$		0			0
$49$		0			0
$50$	−0.449885	+	0.259741i	−0.0636233	+	0.0367329i
$51$		0			0
$52$	1.48943	−	0.859925i	0.206547	−	0.119250i
$53$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$53$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$54$		0			0
$55$			13.3365i			1.79830i
$56$		0			0
$57$		0			0
$58$	−2.07781	+	3.59886i	−0.272829	+	0.472554i
$59$	−2.22966			−0.290277			−0.145139	−	0.989411i	$-0.546363\pi$
$59$	−2.22966			−0.290277			−0.145139	+	0.989411i	$0.546363\pi$
$60$		0			0
$61$			8.99970i			1.15229i	0.817346	+	0.576146i	$0.195444\pi$
$61$			8.99970i			1.15229i	−0.817346	+	0.576146i	$0.804556\pi$
$62$	8.37019			1.06301
$63$		0			0
$64$	−1.00000			−0.125000
$65$			4.04054i			0.501167i
$66$		0			0
$67$	10.8712			1.32813			0.664067	−	0.747673i	$-0.268829\pi$
$67$	10.8712			1.32813			0.664067	+	0.747673i	$0.268829\pi$
$68$	−0.884414	+	1.53185i	−0.107251	+	0.185764i
$69$		0			0
$70$		0			0
$71$		−	4.52106i		−	0.536551i	−0.963342	−	0.268276i	$-0.913546\pi$
$71$		−	4.52106i		−	0.536551i	0.963342	−	0.268276i	$-0.0864538\pi$
$72$		0			0
$73$	4.62660	+	2.67117i	0.541503	+	0.312637i	0.745688	−	0.666295i	$-0.232121\pi$
$73$	4.62660	+	2.67117i	0.541503	+	0.312637i	−0.204185	+	0.978932i	$0.565454\pi$
$74$	7.96547	−	4.59886i	0.925967	−	0.534607i
$75$		0			0
$76$	−0.986680	+	0.569660i	−0.113180	+	0.0653445i
$77$		0			0
$78$		0			0
$79$	−13.0284			−1.46581			−0.732907	−	0.680329i	$-0.761837\pi$
$79$	−13.0284			−1.46581			−0.732907	+	0.680329i	$0.761837\pi$
$80$	1.17468	−	2.03460i	0.131333	−	0.227476i
$81$		0			0
$82$	6.92317	−	3.99709i	0.764536	−	0.441405i
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	0.283758	+	0.958896i	$0.408419\pi$
$83$	−6.27298	+	10.8651i	−0.688549	+	1.19260i	−0.972307	+	0.233707i	$0.924915\pi$
$84$		0			0
$85$	−2.07781	−	3.59886i	−0.225370	−	0.390352i
$86$	−3.04933	−	1.76053i	−0.328817	−	0.189843i
$87$		0			0
$88$	−2.83834	−	4.91614i	−0.302568	−	0.524062i
$89$	0.580529	+	1.00551i	0.0615360	+	0.106583i	0.895152	−	0.445761i	$-0.147067\pi$
$89$	0.580529	+	1.00551i	0.0615360	+	0.106583i	−0.833616	+	0.552344i	$0.813733\pi$
$90$		0			0
$91$		0			0
$92$	3.18272	+	1.83755i	0.331822	+	0.191577i
$93$		0			0
$94$			11.8099i			1.21810i
$95$		−	2.67667i		−	0.274621i
$96$		0			0
$97$	3.97536	+	2.29517i	0.403636	+	0.233039i	0.688052	−	0.725662i	$-0.258466\pi$
$97$	3.97536	+	2.29517i	0.403636	+	0.233039i	−0.284416	+	0.958701i	$0.591800\pi$
$98$		0			0
$99$		0			0
$100$	0.259741	+	0.449885i	0.0259741	+	0.0449885i
$101$	3.31155	+	5.73577i	0.329511	+	0.570730i	0.982415	−	0.186711i	$-0.0597827\pi$
$101$	3.31155	+	5.73577i	0.329511	+	0.570730i	−0.652904	+	0.757441i	$0.726449\pi$
$102$		0			0
$103$	−5.07471	−	2.92989i	−0.500026	−	0.288690i	0.228698	−	0.973497i	$-0.426553\pi$
$103$	−5.07471	−	2.92989i	−0.500026	−	0.288690i	−0.728724	+	0.684807i	$0.759886\pi$
$104$	−0.859925	−	1.48943i	−0.0843225	−	0.146051i
$105$		0			0
$106$		0			0
$107$	4.08386	−	2.35782i	0.394802	−	0.227939i	−0.289437	−	0.957197i	$-0.593468\pi$
$107$	4.08386	−	2.35782i	0.394802	−	0.227939i	0.684239	+	0.729258i	$0.260135\pi$
$108$		0			0
$109$	−2.11835	+	3.66908i	−0.202901	+	0.351435i	−0.949462	−	0.313882i	$-0.898370\pi$
$109$	−2.11835	+	3.66908i	−0.202901	+	0.351435i	0.746561	+	0.665317i	$0.231704\pi$
$110$	13.3365			1.27159
$111$		0			0
$112$		0			0
$113$	−5.91693	+	3.41614i	−0.556618	+	0.321363i	−0.751787	−	0.659406i	$-0.770808\pi$
$113$	−5.91693	+	3.41614i	−0.556618	+	0.321363i	0.195169	+	0.980770i	$0.437474\pi$
$114$		0			0
$115$	−7.47736	+	4.31705i	−0.697267	+	0.402567i
$116$	3.59886	+	2.07781i	0.334146	+	0.192919i
$117$		0			0
$118$			2.22966i			0.205257i
$119$		0			0
$120$		0			0
$121$	10.6123	−	18.3810i	0.964754	−	1.67100i
$122$	8.99970			0.814794
$123$		0			0
$124$		−	8.37019i		−	0.751665i
$125$	10.5263			0.941504
$126$		0			0
$127$	−6.67667			−0.592459			−0.296229	−	0.955117i	$-0.595729\pi$
$127$	−6.67667			−0.592459			−0.296229	+	0.955117i	$0.595729\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	4.04054			0.354379
$131$	3.73653	−	6.47185i	0.326462	−	0.565448i	−0.655345	−	0.755329i	$-0.727477\pi$
$131$	3.73653	−	6.47185i	0.326462	−	0.565448i	0.981807	+	0.189881i	$0.0608102\pi$
$132$		0			0
$133$		0			0
$134$		−	10.8712i		−	0.939133i
$135$		0			0
$136$	1.53185	+	0.884414i	0.131355	+	0.0758379i
$137$	6.91772	−	3.99395i	0.591021	−	0.341226i	−0.174480	−	0.984661i	$-0.555825\pi$
$137$	6.91772	−	3.99395i	0.591021	−	0.341226i	0.765501	+	0.643435i	$0.222491\pi$
$138$		0			0
$139$	−17.9792	+	10.3803i	−1.52498	+	0.880446i	−0.525415	+	0.850846i	$0.676090\pi$
$139$	−17.9792	+	10.3803i	−1.52498	+	0.880446i	−0.999562	+	0.0295993i	$0.990577\pi$
$140$		0			0
$141$		0			0
$142$	−4.52106			−0.379399
$143$	4.88151	−	8.45502i	0.408212	−	0.707044i
$144$		0			0
$145$	−8.45502	+	4.88151i	−0.702151	+	0.405387i
$146$	2.67117	−	4.62660i	0.221068	−	0.382900i
$147$		0			0
$148$	−4.59886	−	7.96547i	−0.378024	−	0.654757i
$149$	−1.03726	−	0.598865i	−0.0849760	−	0.0490609i	0.456910	−	0.889513i	$-0.348956\pi$
$149$	−1.03726	−	0.598865i	−0.0849760	−	0.0490609i	−0.541886	+	0.840452i	$0.682290\pi$
$150$		0			0
$151$	−7.61229	−	13.1849i	−0.619480	−	1.07297i	−0.989581	−	0.143979i	$-0.954010\pi$
$151$	−7.61229	−	13.1849i	−0.619480	−	1.07297i	0.370101	−	0.928991i	$-0.379323\pi$
$152$	0.569660	+	0.986680i	0.0462055	+	0.0800303i
$153$		0			0
$154$		0			0
$155$	17.0300	+	9.83228i	1.36788	+	0.789748i
$156$		0			0
$157$		−	10.0269i		−	0.800237i	−0.916463	−	0.400118i	$-0.868969\pi$
$157$		−	10.0269i		−	0.800237i	0.916463	−	0.400118i	$-0.131031\pi$
$158$			13.0284i			1.03649i
$159$		0			0
$160$	−2.03460	−	1.17468i	−0.160850	−	0.0928665i
$161$		0			0
$162$		0			0
$163$	−6.00158	−	10.3950i	−0.470080	−	0.814202i	0.529335	−	0.848413i	$-0.322442\pi$
$163$	−6.00158	−	10.3950i	−0.470080	−	0.814202i	−0.999415	+	0.0342109i	$0.989108\pi$
$164$	−3.99709	−	6.92317i	−0.312121	−	0.540609i
$165$		0			0
$166$	10.8651	+	6.27298i	0.843297	+	0.486878i
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	0.979681	+	0.200561i	$0.0642765\pi$
$167$	8.57472	+	14.8518i	0.663532	+	1.14927i	−0.316150	+	0.948709i	$0.602390\pi$
$168$		0			0
$169$	−5.02106	+	8.69673i	−0.386235	+	0.668979i
$170$	−3.59886	+	2.07781i	−0.276020	+	0.159360i
$171$		0			0
$172$	−1.76053	+	3.04933i	−0.134239	+	0.232509i
$173$	−1.98748			−0.151105			−0.0755525	−	0.997142i	$-0.524072\pi$
$173$	−1.98748			−0.151105			−0.0755525	+	0.997142i	$0.524072\pi$
$174$		0			0
$175$		0			0
$176$	−4.91614	+	2.83834i	−0.370568	+	0.213948i
$177$		0			0
$178$	1.00551	−	0.580529i	0.0753659	−	0.0435125i
$179$	−7.19773	−	4.15561i	−0.537984	−	0.310605i	0.206278	−	0.978493i	$-0.433865\pi$
$179$	−7.19773	−	4.15561i	−0.537984	−	0.310605i	−0.744261	+	0.667889i	$0.767198\pi$
$180$		0			0
$181$			15.4541i			1.14870i	0.818611	+	0.574348i	$0.194744\pi$
$181$			15.4541i			1.14870i	−0.818611	+	0.574348i	$0.805256\pi$
$182$		0			0
$183$		0			0
$184$	1.83755	−	3.18272i	0.135466	−	0.234634i
$185$	21.6088			1.58871
$186$		0			0
$187$			10.0411i			0.734275i
$188$	11.8099			0.861324
$189$		0			0
$190$	−2.67667			−0.194186
$191$			12.3381i			0.892752i	0.894845	+	0.446376i	$0.147286\pi$
$191$			12.3381i			0.892752i	−0.894845	+	0.446376i	$0.852714\pi$
$192$		0			0
$193$	4.39388			0.316279			0.158139	−	0.987417i	$-0.449451\pi$
$193$	4.39388			0.316279			0.158139	+	0.987417i	$0.449451\pi$
$194$	2.29517	−	3.97536i	0.164784	−	0.285414i
$195$		0			0
$196$		0			0
$197$			10.8865i			0.775632i	0.921737	+	0.387816i	$0.126770\pi$
$197$			10.8865i			0.775632i	−0.921737	+	0.387816i	$0.873230\pi$
$198$		0			0
$199$	23.8733	+	13.7832i	1.69233	+	0.977068i	0.952629	+	0.304135i	$0.0983674\pi$
$199$	23.8733	+	13.7832i	1.69233	+	0.977068i	0.739703	+	0.672933i	$0.234966\pi$
$200$	0.449885	−	0.259741i	0.0318116	−	0.0183665i
$201$		0			0
$202$	5.73577	−	3.31155i	0.403567	−	0.233000i
$203$		0			0
$204$		0			0
$205$	18.7812			1.31174
$206$	−2.92989	+	5.07471i	−0.204135	+	0.353572i
$207$		0			0
$208$	−1.48943	+	0.859925i	−0.103274	+	0.0596250i
$209$	−3.23377	+	5.60106i	−0.223685	+	0.387433i
$210$		0			0
$211$	5.15561	+	8.92978i	0.354927	+	0.614751i	0.987105	−	0.160071i	$-0.0511724\pi$
$211$	5.15561	+	8.92978i	0.354927	+	0.614751i	−0.632179	+	0.774823i	$0.717839\pi$
$212$		0			0
$213$		0			0
$214$	−2.35782	−	4.08386i	−0.161177	−	0.279167i
$215$	−4.13611	−	7.16396i	−0.282081	−	0.488578i
$216$		0			0
$217$		0			0
$218$	3.66908	+	2.11835i	0.248502	+	0.143473i
$219$		0			0
$220$		−	13.3365i		−	0.899149i
$221$			3.04212i			0.204635i
$222$		0			0
$223$	6.24329	+	3.60456i	0.418081	+	0.241379i	0.694256	−	0.719728i	$-0.255733\pi$
$223$	6.24329	+	3.60456i	0.418081	+	0.241379i	−0.276175	+	0.961107i	$0.589067\pi$
$224$		0			0
$225$		0			0
$226$	3.41614	+	5.91693i	0.227238	+	0.393588i
$227$	6.37800	+	11.0470i	0.423323	+	0.733217i	0.996262	−	0.0863812i	$-0.0275303\pi$
$227$	6.37800	+	11.0470i	0.423323	+	0.733217i	−0.572939	+	0.819598i	$0.694197\pi$
$228$		0			0
$229$	3.89208	+	2.24709i	0.257196	+	0.148492i	0.623055	−	0.782178i	$-0.285891\pi$
$229$	3.89208	+	2.24709i	0.257196	+	0.148492i	−0.365859	+	0.930670i	$0.619225\pi$
$230$	4.31705	+	7.47736i	0.284658	+	0.493042i
$231$		0			0
$232$	2.07781	−	3.59886i	0.136415	−	0.236277i
$233$	1.86545	−	1.07702i	0.122210	−	0.0705577i	−0.437649	−	0.899146i	$-0.644189\pi$
$233$	1.86545	−	1.07702i	0.122210	−	0.0705577i	0.559859	+	0.828588i	$0.310855\pi$
$234$		0			0
$235$	−13.8728	+	24.0284i	−0.904963	+	1.56744i
$236$	2.22966			0.145139
$237$		0			0
$238$		0			0
$239$	8.78317	−	5.07096i	0.568136	−	0.328013i	−0.188269	−	0.982118i	$-0.560288\pi$
$239$	8.78317	−	5.07096i	0.568136	−	0.328013i	0.756404	+	0.654104i	$0.226954\pi$
$240$		0			0
$241$	9.13490	−	5.27404i	0.588431	−	0.339731i	−0.176046	−	0.984382i	$-0.556331\pi$
$241$	9.13490	−	5.27404i	0.588431	−	0.339731i	0.764477	+	0.644651i	$0.222997\pi$
$242$	−18.3810	−	10.6123i	−1.18158	−	0.682184i
$243$		0			0
$244$		−	8.99970i		−	0.576146i
$245$		0			0
$246$		0			0
$247$	−0.979729	+	1.69694i	−0.0623387	+	0.107974i
$248$	−8.37019			−0.531507
$249$		0			0
$250$		−	10.5263i		−	0.665744i
$251$	−29.3005			−1.84943			−0.924714	−	0.380662i	$-0.875696\pi$
$251$	−29.3005			−1.84943			−0.924714	+	0.380662i	$0.875696\pi$
$252$		0			0
$253$	20.8623			1.31160
$254$			6.67667i			0.418932i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−3.81430	+	6.60656i	−0.237930	+	0.412106i	−0.960120	−	0.279588i	$-0.909802\pi$
$257$	−3.81430	+	6.60656i	−0.237930	+	0.412106i	0.722190	+	0.691694i	$0.243135\pi$
$258$		0			0
$259$		0			0
$260$		−	4.04054i		−	0.250584i
$261$		0			0
$262$	−6.47185	−	3.73653i	−0.399832	−	0.230843i
$263$	−10.5531	+	6.09281i	−0.650729	+	0.375699i	−0.788736	−	0.614733i	$-0.789264\pi$
$263$	−10.5531	+	6.09281i	−0.650729	+	0.375699i	0.138006	+	0.990431i	$0.455931\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$	−10.8712			−0.664067
$269$	−1.38717	+	2.40264i	−0.0845771	+	0.146492i	−0.905211	−	0.424963i	$-0.860287\pi$
$269$	−1.38717	+	2.40264i	−0.0845771	+	0.146492i	0.820634	+	0.571454i	$0.193621\pi$
$270$		0			0
$271$	2.77815	−	1.60396i	0.168760	−	0.0974338i	−0.413241	−	0.910622i	$-0.635603\pi$
$271$	2.77815	−	1.60396i	0.168760	−	0.0974338i	0.582001	+	0.813188i	$0.302270\pi$
$272$	0.884414	−	1.53185i	0.0536255	−	0.0928821i
$273$		0			0
$274$	−3.99395	−	6.91772i	−0.241283	−	0.417915i
$275$	2.55385	+	1.47446i	0.154003	+	0.0889135i
$276$		0			0
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	0.673925	−	0.738800i	$-0.264607\pi$
$277$	−5.04054	−	8.73047i	−0.302857	−	0.524563i	−0.976782	+	0.214236i	$0.931274\pi$
$278$	10.3803	+	17.9792i	0.622569	+	1.07832i
$279$		0			0
$280$		0			0
$281$	−4.21999	−	2.43641i	−0.251743	−	0.145344i	0.368819	−	0.929501i	$-0.379762\pi$
$281$	−4.21999	−	2.43641i	−0.251743	−	0.145344i	−0.620562	+	0.784157i	$0.713096\pi$
$282$		0			0
$283$			2.81781i			0.167502i	0.996487	+	0.0837508i	$0.0266900\pi$
$283$			2.81781i			0.167502i	−0.996487	+	0.0837508i	$0.973310\pi$
$284$			4.52106i			0.268276i
$285$		0			0
$286$	−8.45502	−	4.88151i	−0.499956	−	0.288650i
$287$		0			0
$288$		0			0
$289$	6.93562	+	12.0129i	0.407978	+	0.706638i
$290$	4.88151	+	8.45502i	0.286652	+	0.496496i
$291$		0			0
$292$	−4.62660	−	2.67117i	−0.270751	−	0.156318i
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	0.722846	−	0.691010i	$-0.242834\pi$
$293$	−4.05694	−	7.02683i	−0.237009	−	0.410512i	−0.959855	+	0.280498i	$0.909500\pi$
$294$		0			0
$295$	−2.61914	+	4.53648i	−0.152492	+	0.264124i
$296$	−7.96547	+	4.59886i	−0.462983	+	0.267304i
$297$		0			0
$298$	−0.598865	+	1.03726i	−0.0346913	+	0.0600871i
$299$	6.32061			0.365530
$300$		0			0
$301$		0			0
$302$	−13.1849	+	7.61229i	−0.758705	+	0.438038i
$303$		0			0
$304$	0.986680	−	0.569660i	0.0565900	−	0.0326722i
$305$	18.3108	+	10.5718i	1.04847	+	0.605337i
$306$		0			0
$307$		−	10.8996i		−	0.622074i	−0.950398	−	0.311037i	$-0.899324\pi$
$307$		−	10.8996i		−	0.622074i	0.950398	−	0.311037i	$-0.100676\pi$
$308$		0			0
$309$		0			0
$310$	9.83228	−	17.0300i	0.558436	−	0.967240i
$311$	−8.23637			−0.467042			−0.233521	−	0.972352i	$-0.575025\pi$
$311$	−8.23637			−0.467042			−0.233521	+	0.972352i	$0.575025\pi$
$312$		0			0
$313$		−	33.8023i		−	1.91062i	−0.295611	−	0.955308i	$-0.595523\pi$
$313$		−	33.8023i		−	1.91062i	0.295611	−	0.955308i	$-0.404477\pi$
$314$	−10.0269			−0.565853
$315$		0			0
$316$	13.0284			0.732907
$317$			6.73090i			0.378045i	0.981973	+	0.189022i	$0.0605319\pi$
$317$			6.73090i			0.378045i	−0.981973	+	0.189022i	$0.939468\pi$
$318$		0			0
$319$	23.5900			1.32079
$320$	−1.17468	+	2.03460i	−0.0656665	+	0.113738i
$321$		0			0
$322$		0			0
$323$		−	2.01526i		−	0.112132i
$324$		0			0
$325$	0.773734	+	0.446715i	0.0429190	+	0.0247793i
$326$	−10.3950	+	6.00158i	−0.575728	+	0.332397i
$327$		0			0
$328$	−6.92317	+	3.99709i	−0.382268	+	0.220703i
$329$		0			0
$330$		0			0
$331$	−32.0569			−1.76200			−0.881002	−	0.473112i	$-0.843131\pi$
$331$	−32.0569			−1.76200			−0.881002	+	0.473112i	$0.843131\pi$
$332$	6.27298	−	10.8651i	0.344275	−	0.596301i
$333$		0			0
$334$	14.8518	−	8.57472i	0.812657	−	0.469188i
$335$	12.7702	−	22.1187i	0.697712	−	1.20847i
$336$		0			0
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	−0.980668	−	0.195681i	$-0.937308\pi$
$337$	−12.1123	−	20.9791i	−0.659799	−	1.14280i	0.320869	−	0.947124i	$-0.396025\pi$
$338$	8.69673	+	5.02106i	0.473040	+	0.273110i
$339$		0			0
$340$	2.07781	+	3.59886i	0.112685	+	0.195176i
$341$	−23.7574	−	41.1490i	−1.28654	−	2.22834i
$342$		0			0
$343$		0			0
$344$	3.04933	+	1.76053i	0.164409	+	0.0949214i
$345$		0			0
$346$			1.98748i			0.106847i
$347$		−	22.7999i		−	1.22396i	−0.790873	−	0.611981i	$-0.790373\pi$
$347$		−	22.7999i		−	1.22396i	0.790873	−	0.611981i	$-0.209627\pi$
$348$		0			0
$349$	2.46389	+	1.42253i	0.131889	+	0.0761461i	0.564493	−	0.825438i	$-0.309072\pi$
$349$	2.46389	+	1.42253i	0.131889	+	0.0761461i	−0.432604	+	0.901584i	$0.642405\pi$
$350$		0			0
$351$		0			0
$352$	2.83834	+	4.91614i	0.151284	+	0.262031i
$353$	−3.57212	−	6.18709i	−0.190125	−	0.329306i	0.755167	−	0.655533i	$-0.227556\pi$
$353$	−3.57212	−	6.18709i	−0.190125	−	0.329306i	−0.945291	+	0.326227i	$0.894223\pi$
$354$		0			0
$355$	−9.19856	−	5.31079i	−0.488209	−	0.281868i
$356$	−0.580529	−	1.00551i	−0.0307680	−	0.0532917i
$357$		0			0
$358$	−4.15561	+	7.19773i	−0.219631	+	0.380412i
$359$	10.0491	−	5.80186i	0.530372	−	0.306210i	−0.210796	−	0.977530i	$-0.567606\pi$
$359$	10.0491	−	5.80186i	0.530372	−	0.306210i	0.741168	+	0.671320i	$0.234272\pi$
$360$		0			0
$361$	−8.85097	+	15.3303i	−0.465841	+	0.806860i
$362$	15.4541			0.812250
$363$		0			0
$364$		0			0
$365$	10.8695	−	6.27554i	0.568938	−	0.328477i
$366$		0			0
$367$	6.78525	−	3.91747i	0.354187	−	0.204490i	−0.312341	−	0.949970i	$-0.601113\pi$
$367$	6.78525	−	3.91747i	0.354187	−	0.204490i	0.666528	+	0.745480i	$0.267780\pi$
$368$	−3.18272	−	1.83755i	−0.165911	−	0.0957887i
$369$		0			0
$370$		−	21.6088i		−	1.12339i
$371$		0			0
$372$		0			0
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	0.314905	+	0.949123i	$0.398027\pi$
$373$	−12.8339	+	22.2289i	−0.664512	+	1.15097i	−0.979417	+	0.201845i	$0.935306\pi$
$374$	10.0411			0.519211
$375$		0			0
$376$		−	11.8099i		−	0.609048i
$377$	7.14702			0.368091
$378$		0			0
$379$	−15.1045			−0.775868			−0.387934	−	0.921687i	$-0.626811\pi$
$379$	−15.1045			−0.775868			−0.387934	+	0.921687i	$0.626811\pi$
$380$			2.67667i			0.137310i
$381$		0			0
$382$	12.3381			0.631271
$383$	0.763322	−	1.32211i	0.0390040	−	0.0675568i	−0.845864	−	0.533398i	$-0.820915\pi$
$383$	0.763322	−	1.32211i	0.0390040	−	0.0675568i	0.884868	+	0.465841i	$0.154248\pi$
$384$		0			0
$385$		0			0
$386$		−	4.39388i		−	0.223643i
$387$		0			0
$388$	−3.97536	−	2.29517i	−0.201818	−	0.116520i
$389$	12.8948	−	7.44483i	0.653794	−	0.377468i	−0.136115	−	0.990693i	$-0.543462\pi$
$389$	12.8948	−	7.44483i	0.653794	−	0.377468i	0.789908	+	0.613225i	$0.210128\pi$
$390$		0			0
$391$	−5.62969	+	3.25030i	−0.284706	+	0.164375i
$392$		0			0
$393$		0			0
$394$	10.8865			0.548454
$395$	−15.3042	+	26.5077i	−0.770039	+	1.33375i
$396$		0			0
$397$	−24.9302	+	14.3935i	−1.25121	+	0.722388i	−0.971350	−	0.237653i	$-0.923622\pi$
$397$	−24.9302	+	14.3935i	−1.25121	+	0.722388i	−0.279862	+	0.960040i	$0.590289\pi$
$398$	13.7832	−	23.8733i	0.690892	−	1.19666i
$399$		0			0
$400$	−0.259741	−	0.449885i	−0.0129871	−	0.0224942i
$401$	−33.0592	−	19.0868i	−1.65090	−	0.953147i	−0.976703	−	0.214595i	$-0.931157\pi$
$401$	−33.0592	−	19.0868i	−1.65090	−	0.953147i	−0.674196	−	0.738552i	$-0.735510\pi$
$402$		0			0
$403$	−7.19773	−	12.4668i	−0.358544	−	0.621017i
$404$	−3.31155	−	5.73577i	−0.164756	−	0.285365i
$405$		0			0
$406$		0			0
$407$	−45.2173	−	26.1062i	−2.24134	−	1.29404i
$408$		0			0
$409$		−	6.96694i		−	0.344493i	−0.985054	−	0.172247i	$-0.944897\pi$
$409$		−	6.96694i		−	0.344493i	0.985054	−	0.172247i	$-0.0551026\pi$
$410$		−	18.7812i		−	0.927538i
$411$		0			0
$412$	5.07471	+	2.92989i	0.250013	+	0.144345i
$413$		0			0
$414$		0			0
$415$	14.7375	+	25.5261i	0.723435	+	1.25303i
$416$	0.859925	+	1.48943i	0.0421613	+	0.0730255i
$417$		0			0
$418$	5.60106	+	3.23377i	0.273957	+	0.158169i
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	−0.880146	−	0.474702i	$-0.842556\pi$
$419$	−17.4232	−	30.1778i	−0.851177	−	1.47428i	0.0289690	−	0.999580i	$-0.490778\pi$
$420$		0			0
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	−0.788302	−	0.615288i	$-0.789040\pi$
$421$	2.84597	−	4.92936i	0.138704	−	0.240242i	0.927006	+	0.375046i	$0.122373\pi$
$422$	8.92978	−	5.15561i	0.434695	−	0.250971i
$423$		0			0
$424$		0			0
$425$	−0.918875			−0.0445720
$426$		0			0
$427$		0			0
$428$	−4.08386	+	2.35782i	−0.197401	+	0.113969i
$429$		0			0
$430$	−7.16396	+	4.13611i	−0.345477	+	0.199461i
$431$	26.2350	+	15.1468i	1.26370	+	0.729595i	0.973787	−	0.227460i	$-0.0730420\pi$
$431$	26.2350	+	15.1468i	1.26370	+	0.729595i	0.289908	+	0.957055i	$0.406375\pi$
$432$		0			0
$433$		−	23.6094i		−	1.13459i	−0.823513	−	0.567297i	$-0.807989\pi$
$433$		−	23.6094i		−	1.13459i	0.823513	−	0.567297i	$-0.192011\pi$
$434$		0			0
$435$		0			0
$436$	2.11835	−	3.66908i	0.101450	−	0.175717i
$437$	−4.18711			−0.200297
$438$		0			0
$439$			25.0202i			1.19415i	0.802185	+	0.597075i	$0.203671\pi$
$439$			25.0202i			1.19415i	−0.802185	+	0.597075i	$0.796329\pi$
$440$	−13.3365			−0.635794
$441$		0			0
$442$	3.04212			0.144699
$443$		−	23.0300i		−	1.09419i	−0.837071	−	0.547094i	$-0.815734\pi$
$443$		−	23.0300i		−	1.09419i	0.837071	−	0.547094i	$-0.184266\pi$
$444$		0			0
$445$	2.72774			0.129307
$446$	3.60456	−	6.24329i	0.170681	−	0.295628i
$447$		0			0
$448$		0			0
$449$			15.9028i			0.750501i	0.926923	+	0.375251i	$0.122443\pi$
$449$			15.9028i			0.750501i	−0.926923	+	0.375251i	$0.877557\pi$
$450$		0			0
$451$	−39.3006	−	22.6902i	−1.85059	−	1.06844i
$452$	5.91693	−	3.41614i	0.278309	−	0.160682i
$453$		0			0
$454$	11.0470	−	6.37800i	0.518462	−	0.299334i
$455$		0			0
$456$		0			0
$457$	−5.66614			−0.265051			−0.132525	−	0.991180i	$-0.542309\pi$
$457$	−5.66614			−0.265051			−0.132525	+	0.991180i	$0.542309\pi$
$458$	2.24709	−	3.89208i	0.105000	−	0.181865i
$459$		0			0
$460$	7.47736	−	4.31705i	0.348634	−	0.201284i
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	0.223194	+	0.974774i	$0.428352\pi$
$461$	−15.7292	+	27.2438i	−0.732582	+	1.26887i	−0.955776	+	0.294095i	$0.904982\pi$
$462$		0			0
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	0.952192	−	0.305500i	$-0.0988236\pi$
$463$	4.55148	+	7.88340i	0.211525	+	0.366373i	−0.740667	+	0.671873i	$0.765490\pi$
$464$	−3.59886	−	2.07781i	−0.167073	−	0.0964597i
$465$		0			0
$466$	−1.07702	−	1.86545i	−0.0498918	−	0.0864152i
$467$	15.1516	+	26.2433i	0.701132	+	1.21440i	0.968069	+	0.250682i	$0.0806549\pi$
$467$	15.1516	+	26.2433i	0.701132	+	1.21440i	−0.266938	+	0.963714i	$0.586012\pi$
$468$		0			0
$469$		0			0
$470$	24.0284	+	13.8728i	1.10835	+	0.639906i
$471$		0			0
$472$		−	2.22966i		−	0.102628i
$473$			19.9879i			0.919044i
$474$		0			0
$475$	−0.512563	−	0.295928i	−0.0235180	−	0.0135781i
$476$		0			0
$477$		0			0
$478$	−5.07096	−	8.78317i	−0.231940	−	0.401733i
$479$	−2.33143	−	4.03816i	−0.106526	−	0.184508i	0.807835	−	0.589409i	$-0.200639\pi$
$479$	−2.33143	−	4.03816i	−0.106526	−	0.184508i	−0.914361	+	0.404901i	$0.867306\pi$
$480$		0			0
$481$	−13.6994	−	7.90935i	−0.624639	−	0.360636i
$482$	−5.27404	−	9.13490i	−0.240226	−	0.416083i
$483$		0			0
$484$	−10.6123	+	18.3810i	−0.482377	+	0.835501i
$485$	9.33953	−	5.39218i	0.424086	−	0.244846i
$486$		0			0
$487$	9.74105	−	16.8720i	0.441409	−	0.764543i	−0.556385	−	0.830924i	$-0.687812\pi$
$487$	9.74105	−	16.8720i	0.441409	−	0.764543i	0.997794	+	0.0663816i	$0.0211455\pi$
$488$	−8.99970			−0.407397
$489$		0			0
$490$		0			0
$491$	17.7437	−	10.2443i	0.800762	−	0.462320i	−0.0429758	−	0.999076i	$-0.513684\pi$
$491$	17.7437	−	10.2443i	0.800762	−	0.462320i	0.843737	+	0.536756i	$0.180351\pi$
$492$		0			0
$493$	−6.36577	+	3.67528i	−0.286700	+	0.165526i
$494$	1.69694	+	0.979729i	0.0763490	+	0.0440801i
$495$		0			0
$496$			8.37019i			0.375832i
$497$		0			0
$498$		0			0
$499$	5.12598	−	8.87845i	0.229470	−	0.397454i	−0.728181	−	0.685385i	$-0.759634\pi$
$499$	5.12598	−	8.87845i	0.229470	−	0.397454i	0.957651	+	0.287931i	$0.0929673\pi$
$500$	−10.5263			−0.470752
$501$		0			0
$502$			29.3005i			1.30774i
$503$	−14.5521			−0.648845			−0.324422	−	0.945912i	$-0.605170\pi$
$503$	−14.5521			−0.648845			−0.324422	+	0.945912i	$0.605170\pi$
$504$		0			0
$505$	15.5600			0.692412
$506$		−	20.8623i		−	0.927442i
$507$		0			0
$508$	6.67667			0.296229
$509$	−16.6617	+	28.8589i	−0.738517	+	1.27915i	0.214646	+	0.976692i	$0.431140\pi$
$509$	−16.6617	+	28.8589i	−0.738517	+	1.27915i	−0.953163	+	0.302457i	$0.902193\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	6.60656	+	3.81430i	0.291403	+	0.168242i
$515$	−11.9223	+	6.88335i	−0.525360	+	0.303317i
$516$		0			0
$517$	58.0591	−	33.5204i	2.55343	−	1.47423i
$518$		0			0
$519$		0			0
$520$	−4.04054			−0.177189
$521$	3.26963	−	5.66316i	0.143245	−	0.248108i	−0.785472	−	0.618897i	$-0.787580\pi$
$521$	3.26963	−	5.66316i	0.143245	−	0.248108i	0.928717	+	0.370790i	$0.120913\pi$
$522$		0			0
$523$	0.681439	−	0.393429i	0.0297972	−	0.0172034i	−0.485027	−	0.874499i	$-0.661190\pi$
$523$	0.681439	−	0.393429i	0.0297972	−	0.0172034i	0.514825	+	0.857296i	$0.327857\pi$
$524$	−3.73653	+	6.47185i	−0.163231	+	0.282724i
$525$		0			0
$526$	6.09281	+	10.5531i	0.265659	+	0.460135i
$527$	12.8219	+	7.40271i	0.558530	+	0.322467i
$528$		0			0
$529$	−4.74685	−	8.22178i	−0.206385	−	0.357469i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−11.9068	−	6.87440i	−0.515741	−	0.297763i
$534$		0			0
$535$		−	11.0787i		−	0.478975i
$536$			10.8712i			0.469566i
$537$		0			0
$538$	2.40264	+	1.38717i	0.103585	+	0.0598050i
$539$		0			0
$540$		0			0
$541$	−2.80227	−	4.85367i	−0.120479	−	0.208676i	0.799478	−	0.600696i	$-0.205110\pi$
$541$	−2.80227	−	4.85367i	−0.120479	−	0.208676i	−0.919957	+	0.392020i	$0.871776\pi$
$542$	−1.60396	−	2.77815i	−0.0688961	−	0.119332i
$543$		0			0
$544$	−1.53185	−	0.884414i	−0.0656775	−	0.0379189i
$545$	4.97675	+	8.61999i	0.213181	+	0.369240i
$546$		0			0
$547$	−6.91456	+	11.9764i	−0.295645	+	0.512073i	−0.975135	−	0.221612i	$-0.928868\pi$
$547$	−6.91456	+	11.9764i	−0.295645	+	0.512073i	0.679489	+	0.733685i	$0.262201\pi$
$548$	−6.91772	+	3.99395i	−0.295510	+	0.170613i
$549$		0			0
$550$	1.47446	−	2.55385i	0.0628714	−	0.108896i
$551$	−4.73457			−0.201700
$552$		0			0
$553$		0			0
$554$	−8.73047	+	5.04054i	−0.370922	+	0.214152i
$555$		0			0
$556$	17.9792	−	10.3803i	0.762488	−	0.440223i
$557$	−24.0957	−	13.9117i	−1.02097	−	0.589456i	−0.106584	−	0.994304i	$-0.533991\pi$
$557$	−24.0957	−	13.9117i	−1.02097	−	0.589456i	−0.914384	+	0.404848i	$0.867325\pi$
$558$		0			0
$559$			6.05569i			0.256128i
$560$		0			0
$561$		0			0
$562$	−2.43641	+	4.21999i	−0.102774	+	0.178009i
$563$	−24.5300			−1.03382			−0.516909	−	0.856040i	$-0.672917\pi$
$563$	−24.5300			−1.03382			−0.516909	+	0.856040i	$0.672917\pi$
$564$		0			0
$565$			16.0515i			0.675291i
$566$	2.81781			0.118441
$567$		0			0
$568$	4.52106			0.189699
$569$		−	27.1079i		−	1.13642i	−0.822882	−	0.568212i	$-0.807635\pi$
$569$		−	27.1079i		−	1.13642i	0.822882	−	0.568212i	$-0.192365\pi$
$570$		0			0
$571$	−29.8354			−1.24857			−0.624287	−	0.781195i	$-0.714610\pi$
$571$	−29.8354			−1.24857			−0.624287	+	0.781195i	$0.714610\pi$
$572$	−4.88151	+	8.45502i	−0.204106	+	0.353522i
$573$		0			0
$574$		0			0
$575$			1.90915i			0.0796169i
$576$		0			0
$577$	−24.3930	−	14.0833i	−1.01549	−	0.586296i	−0.102699	−	0.994712i	$-0.532748\pi$
$577$	−24.3930	−	14.0833i	−1.01549	−	0.586296i	−0.912796	+	0.408416i	$0.866081\pi$
$578$	12.0129	−	6.93562i	0.499669	−	0.288484i
$579$		0			0
$580$	8.45502	−	4.88151i	0.351076	−	0.202694i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	−2.67117	+	4.62660i	−0.110534	+	0.191450i
$585$		0			0
$586$	−7.02683	+	4.05694i	−0.290276	+	0.167591i
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	−0.745343	−	0.666681i	$-0.767714\pi$
$587$	4.95928	−	8.58973i	0.204692	−	0.354536i	0.950034	+	0.312145i	$0.101048\pi$
$588$		0			0
$589$	4.76816	+	8.25870i	0.196469	+	0.340294i
$590$	4.53648	+	2.61914i	0.186764	+	0.107828i
$591$		0			0
$592$	4.59886	+	7.96547i	0.189012	+	0.327379i
$593$	2.34936	+	4.06921i	0.0964766	+	0.167102i	0.910224	−	0.414116i	$-0.135909\pi$
$593$	2.34936	+	4.06921i	0.0964766	+	0.167102i	−0.813747	+	0.581219i	$0.802576\pi$
$594$		0			0
$595$		0			0
$596$	1.03726	+	0.598865i	0.0424880	+	0.0245305i
$597$		0			0
$598$		−	6.32061i		−	0.258469i
$599$		−	14.7004i		−	0.600641i	−0.953838	−	0.300320i	$-0.902906\pi$
$599$		−	14.7004i		−	0.600641i	0.953838	−	0.300320i	$-0.0970936\pi$
$600$		0			0
$601$	−16.2923	−	9.40634i	−0.664575	−	0.383693i	0.129443	−	0.991587i	$-0.458681\pi$
$601$	−16.2923	−	9.40634i	−0.664575	−	0.383693i	−0.794018	+	0.607894i	$0.792014\pi$
$602$		0			0
$603$		0			0
$604$	7.61229	+	13.1849i	0.309740	+	0.536485i
$605$	−24.9321	−	43.1836i	−1.01363	−	1.75566i
$606$		0			0
$607$	10.9051	+	6.29608i	0.442625	+	0.255550i	0.704711	−	0.709495i	$-0.251077\pi$
$607$	10.9051	+	6.29608i	0.442625	+	0.255550i	−0.262085	+	0.965045i	$0.584410\pi$
$608$	−0.569660	−	0.986680i	−0.0231028	−	0.0400152i
$609$		0			0
$610$	10.5718	−	18.3108i	0.428038	−	0.741383i
$611$	17.5900	−	10.1556i	0.711617	−	0.410852i
$612$		0			0
$613$	4.91009	−	8.50452i	0.198317	−	0.343494i	−0.749666	−	0.661816i	$-0.769786\pi$
$613$	4.91009	−	8.50452i	0.198317	−	0.343494i	0.947983	+	0.318322i	$0.103119\pi$
$614$	−10.8996			−0.439873
$615$		0			0
$616$		0			0
$617$	3.25158	−	1.87730i	0.130904	−	0.0755772i	−0.433118	−	0.901337i	$-0.642587\pi$
$617$	3.25158	−	1.87730i	0.130904	−	0.0755772i	0.564022	+	0.825760i	$0.309253\pi$
$618$		0			0
$619$	9.56902	−	5.52468i	0.384611	−	0.222055i	−0.295211	−	0.955432i	$-0.595390\pi$
$619$	9.56902	−	5.52468i	0.384611	−	0.222055i	0.679823	+	0.733376i	$0.262057\pi$
$620$	−17.0300	−	9.83228i	−0.683942	−	0.394874i
$621$		0			0
$622$			8.23637i			0.330248i
$623$		0			0
$624$		0			0
$625$	13.6638	−	23.6664i	0.546551	−	0.946654i
$626$	−33.8023			−1.35101
$627$		0			0
$628$			10.0269i			0.400118i
$629$	16.2692			0.648696
$630$		0			0
$631$	19.4921			0.775969			0.387984	−	0.921666i	$-0.373171\pi$
$631$	19.4921			0.775969			0.387984	+	0.921666i	$0.373171\pi$
$632$		−	13.0284i		−	0.518243i
$633$		0			0
$634$	6.73090			0.267318
$635$	−7.84294	+	13.5844i	−0.311238	+	0.539080i
$636$		0			0
$637$		0			0
$638$		−	23.5900i		−	0.933938i
$639$		0			0
$640$	2.03460	+	1.17468i	0.0804248	+	0.0464333i
$641$	−22.6669	+	13.0868i	−0.895290	+	0.516896i	−0.875669	−	0.482912i	$-0.839579\pi$
$641$	−22.6669	+	13.0868i	−0.895290	+	0.516896i	−0.0196208	+	0.999807i	$0.506246\pi$
$642$		0			0
$643$	−9.50955	+	5.49034i	−0.375020	+	0.216518i	−0.675649	−	0.737223i	$-0.736137\pi$
$643$	−9.50955	+	5.49034i	−0.375020	+	0.216518i	0.300629	+	0.953741i	$0.402803\pi$
$644$		0			0
$645$		0			0
$646$	−2.01526			−0.0792894
$647$	−16.0063	+	27.7237i	−0.629273	+	1.08993i	0.358425	+	0.933558i	$0.383314\pi$
$647$	−16.0063	+	27.7237i	−0.629273	+	1.08993i	−0.987698	+	0.156374i	$0.950019\pi$
$648$		0			0
$649$	10.9613	−	6.32852i	0.430270	−	0.248416i
$650$	0.446715	−	0.773734i	0.0175216	−	0.0303483i
$651$		0			0
$652$	6.00158	+	10.3950i	0.235040	+	0.407101i
$653$	19.3686	+	11.1825i	0.757952	+	0.437604i	0.828560	−	0.559900i	$-0.189161\pi$
$653$	19.3686	+	11.1825i	0.757952	+	0.437604i	−0.0706080	+	0.997504i	$0.522494\pi$
$654$		0			0
$655$	−8.77843	−	15.2047i	−0.343002	−	0.594097i
$656$	3.99709	+	6.92317i	0.156060	+	0.270304i
$657$		0			0
$658$		0			0
$659$	19.2546	+	11.1166i	0.750053	+	0.433043i	0.825713	−	0.564091i	$-0.190773\pi$
$659$	19.2546	+	11.1166i	0.750053	+	0.433043i	−0.0756603	+	0.997134i	$0.524106\pi$
$660$		0			0
$661$			10.5499i			0.410343i	0.978726	+	0.205171i	$0.0657751\pi$
$661$			10.5499i			0.410343i	−0.978726	+	0.205171i	$0.934225\pi$
$662$			32.0569i			1.24593i
$663$		0			0
$664$	−10.8651	−	6.27298i	−0.421649	−	0.243439i
$665$		0			0
$666$		0			0
$667$	7.63613	+	13.2262i	0.295672	+	0.512119i
$668$	−8.57472	−	14.8518i	−0.331766	−	0.574635i
$669$		0			0
$670$	−22.1187	−	12.7702i	−0.854519	−	0.493357i
$671$	−25.5442	−	44.2438i	−0.986121	−	1.70801i
$672$		0			0
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	−0.608498	−	0.793555i	$-0.708228\pi$
$673$	9.93562	−	17.2090i	0.382990	−	0.663358i	0.991488	+	0.130197i	$0.0415610\pi$
$674$	−20.9791	+	12.1123i	−0.808085	+	0.466548i
$675$		0			0
$676$	5.02106	−	8.69673i	0.193118	−	0.334490i
$677$	15.9290			0.612201			0.306100	−	0.951999i	$-0.400976\pi$
$677$	15.9290			0.612201			0.306100	+	0.951999i	$0.400976\pi$
$678$		0			0
$679$		0			0
$680$	3.59886	−	2.07781i	0.138010	−	0.0796802i
$681$		0			0
$682$	−41.1490	+	23.7574i	−1.57568	+	0.909718i
$683$	16.4777	+	9.51343i	0.630503	+	0.364021i	0.780947	−	0.624597i	$-0.214737\pi$
$683$	16.4777	+	9.51343i	0.630503	+	0.364021i	−0.150444	+	0.988619i	$0.548070\pi$
$684$		0			0
$685$		−	18.7664i		−	0.717028i
$686$		0			0
$687$		0			0
$688$	1.76053	−	3.04933i	0.0671196	−	0.116254i
$689$		0			0
$690$		0			0
$691$			0.161055i			0.00612681i	0.999995	+	0.00306340i	$0.000975113\pi$
$691$			0.161055i			0.00612681i	−0.999995	+	0.00306340i	$0.999025\pi$
$692$	1.98748			0.0755525
$693$		0			0
$694$	−22.7999			−0.865471
$695$			48.7741i			1.85011i
$696$		0			0
$697$	14.1403			0.535604
$698$	1.42253	−	2.46389i	0.0538434	−	0.0932595i
$699$		0			0
$700$		0			0
$701$			9.98234i			0.377028i	0.982071	+	0.188514i	$0.0603670\pi$
$701$			9.98234i			0.377028i	−0.982071	+	0.188514i	$0.939633\pi$
$702$		0			0
$703$	9.07522	+	5.23958i	0.342278	+	0.197614i
$704$	4.91614	−	2.83834i	0.185284	−	0.106974i
$705$		0			0
$706$	−6.18709	+	3.57212i	−0.232854	+	0.134438i
$707$		0			0
$708$		0			0
$709$	−24.3923			−0.916072			−0.458036	−	0.888934i	$-0.651447\pi$
$709$	−24.3923			−0.916072			−0.458036	+	0.888934i	$0.651447\pi$
$710$	−5.31079	+	9.19856i	−0.199311	+	0.345216i
$711$		0			0
$712$	−1.00551	+	0.580529i	−0.0376829	+	0.0217563i
$713$	15.3806	−	26.6400i	0.576008	−	0.997676i
$714$		0			0
$715$	−11.4684	−	19.8639i	−0.428894	−	0.742867i
$716$	7.19773	+	4.15561i	0.268992	+	0.155302i
$717$		0			0
$718$	−5.80186	−	10.0491i	−0.216523	−	0.375030i
$719$	8.13460	+	14.0895i	0.303370	+	0.525451i	0.976897	−	0.213711i	$-0.0685550\pi$
$719$	8.13460	+	14.0895i	0.303370	+	0.525451i	−0.673527	+	0.739162i	$0.735222\pi$
$720$		0			0
$721$		0			0
$722$	15.3303	+	8.85097i	0.570536	+	0.329399i
$723$		0			0
$724$		−	15.4541i		−	0.574348i
$725$			2.15877i			0.0801745i
$726$		0			0
$727$	−20.6626	−	11.9296i	−0.766335	−	0.442444i	0.0652306	−	0.997870i	$-0.479222\pi$
$727$	−20.6626	−	11.9296i	−0.766335	−	0.442444i	−0.831566	+	0.555427i	$0.812555\pi$
$728$		0			0
$729$		0			0
$730$	−6.27554	−	10.8695i	−0.232268	−	0.402300i
$731$	−3.11408	−	5.39374i	−0.115178	−	0.199495i
$732$		0			0
$733$	10.6259	+	6.13486i	0.392476	+	0.226596i	0.683233	−	0.730201i	$-0.260574\pi$
$733$	10.6259	+	6.13486i	0.392476	+	0.226596i	−0.290756	+	0.956797i	$0.593907\pi$
$734$	−3.91747	−	6.78525i	−0.144596	−	0.250448i
$735$		0			0
$736$	−1.83755	+	3.18272i	−0.0677329	+	0.117317i
$737$	−53.4446	+	30.8562i	−1.96866	+	1.13660i
$738$		0			0
$739$	−20.9446	+	36.2771i	−0.770459	+	1.33447i	0.166853	+	0.985982i	$0.446639\pi$
$739$	−20.9446	+	36.2771i	−0.770459	+	1.33447i	−0.937312	+	0.348492i	$0.886694\pi$
$740$	−21.6088			−0.794354
$741$		0			0
$742$		0			0
$743$	−43.9160	+	25.3549i	−1.61112	+	0.930182i	−0.622011	+	0.783008i	$0.713684\pi$
$743$	−43.9160	+	25.3549i	−1.61112	+	0.930182i	−0.989111	+	0.147173i	$0.952982\pi$
$744$		0			0
$745$	−2.43690	+	1.40695i	−0.0892813	+	0.0515466i
$746$	22.2289	+	12.8339i	0.813858	+	0.469881i
$747$		0			0
$748$		−	10.0411i		−	0.367137i
$749$		0			0
$750$		0			0
$751$	16.3683	−	28.3508i	0.597289	−	1.03454i	−0.395930	−	0.918281i	$-0.629578\pi$
$751$	16.3683	−	28.3508i	0.597289	−	1.03454i	0.993219	−	0.116255i	$-0.0370890\pi$
$752$	−11.8099			−0.430662
$753$		0			0
$754$		−	7.14702i		−	0.260279i
$755$	−35.7680			−1.30173
$756$		0			0
$757$	−17.9255			−0.651512			−0.325756	−	0.945454i	$-0.605619\pi$
$757$	−17.9255			−0.651512			−0.325756	+	0.945454i	$0.605619\pi$
$758$			15.1045i			0.548622i
$759$		0			0
$760$	2.67667			0.0970930
$761$	21.8509	−	37.8469i	0.792096	−	1.37195i	−0.132571	−	0.991174i	$-0.542323\pi$
$761$	21.8509	−	37.8469i	0.792096	−	1.37195i	0.924667	−	0.380777i	$-0.124343\pi$
$762$		0			0
$763$		0			0
$764$		−	12.3381i		−	0.446376i
$765$		0			0
$766$	−1.32211	−	0.763322i	−0.0477699	−	0.0275800i
$767$	3.32093	−	1.91734i	0.119912	−	0.0692311i
$768$		0			0
$769$	37.0864	−	21.4118i	1.33737	−	0.772131i	0.350953	−	0.936393i	$-0.385858\pi$
$769$	37.0864	−	21.4118i	1.33737	−	0.772131i	0.986417	+	0.164262i	$0.0525242\pi$
$770$		0			0
$771$		0			0
$772$	−4.39388			−0.158139
$773$	10.8025	−	18.7105i	0.388540	−	0.672971i	−0.603714	−	0.797201i	$-0.706313\pi$
$773$	10.8025	−	18.7105i	0.388540	−	0.672971i	0.992253	+	0.124231i	$0.0396462\pi$
$774$		0			0
$775$	3.76562	−	2.17408i	0.135265	−	0.0780953i
$776$	−2.29517	+	3.97536i	−0.0823919	+	0.142707i
$777$		0			0
$778$	−7.44483	−	12.8948i	−0.266910	−	0.462302i
$779$	7.88771	+	4.55397i	0.282606	+	0.163163i
$780$		0			0
$781$	12.8323	+	22.2262i	0.459175	+	0.795315i
$782$	3.25030	+	5.62969i	0.116231	+	0.201317i
$783$		0			0
$784$		0			0
$785$	−20.4008	−	11.7784i	−0.728137	−	0.420390i
$786$		0			0
$787$			51.3042i			1.82880i	0.404817	+	0.914398i	$0.367335\pi$
$787$			51.3042i			1.82880i	−0.404817	+	0.914398i	$0.632665\pi$
$788$		−	10.8865i		−	0.387816i
$789$		0			0
$790$	26.5077	+	15.3042i	0.943102	+	0.544500i
$791$		0			0
$792$		0			0
$793$	−7.73906	−	13.4044i	−0.274822	−	0.476006i
$794$	14.3935	+	24.9302i	0.510805	+	0.884740i
$795$		0			0
$796$	−23.8733	−	13.7832i	−0.846166	−	0.488534i
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	0.849662	−	0.527327i	$-0.176806\pi$
$797$	−0.899094	−	1.55728i	−0.0318476	−	0.0551616i	−0.881510	+	0.472166i	$0.843472\pi$
$798$		0			0
$799$	−10.4448	+	18.0910i	−0.369512	+	0.640013i
$800$	−0.449885	+	0.259741i	−0.0159058	+	0.00918323i
$801$		0			0
$802$	−19.0868	+	33.0592i	−0.673977	+	1.16736i
$803$	−30.3267			−1.07021
$804$		0			0
$805$		0			0
$806$	−12.4668	+	7.19773i	−0.439125	+	0.253529i
$807$		0			0
$808$	−5.73577	+	3.31155i	−0.201784	+	0.116500i
$809$	−35.2371	−	20.3441i	−1.23887	−	0.715262i	−0.270006	−	0.962859i	$-0.587026\pi$
$809$	−35.2371	−	20.3441i	−1.23887	−	0.715262i	−0.968863	+	0.247597i	$0.920359\pi$
$810$		0			0
$811$			0.378710i			0.0132983i	0.999978	+	0.00664916i	$0.00211651\pi$
$811$			0.378710i			0.0132983i	−0.999978	+	0.00664916i	$0.997883\pi$
$812$		0			0
$813$		0			0
$814$	−26.1062	+	45.2173i	−0.915023	+	1.58487i
$815$	−28.1997			−0.987793
$816$		0			0
$817$		−	4.01161i		−	0.140349i
$818$	−6.96694			−0.243593
$819$		0			0
$820$	−18.7812			−0.655868
$821$			13.2754i			0.463315i	0.972797	+	0.231658i	$0.0744149\pi$
$821$			13.2754i			0.463315i	−0.972797	+	0.231658i	$0.925585\pi$
$822$		0			0
$823$	27.7422			0.967034			0.483517	−	0.875335i	$-0.339359\pi$
$823$	27.7422			0.967034			0.483517	+	0.875335i	$0.339359\pi$
$824$	2.92989	−	5.07471i	0.102067	−	0.176786i
$825$		0			0
$826$		0			0
$827$			27.7183i			0.963859i	0.876210	+	0.481929i	$0.160064\pi$
$827$			27.7183i			0.963859i	−0.876210	+	0.481929i	$0.839936\pi$
$828$		0			0
$829$	−37.0105	−	21.3680i	−1.28543	−	0.742143i	−0.307593	−	0.951518i	$-0.599524\pi$
$829$	−37.0105	−	21.3680i	−1.28543	−	0.742143i	−0.977835	+	0.209375i	$0.932857\pi$
$830$	25.5261	−	14.7375i	0.886023	−	0.511545i
$831$		0			0
$832$	1.48943	−	0.859925i	0.0516368	−	0.0298125i
$833$		0			0
$834$		0			0
$835$	40.2902			1.39430
$836$	3.23377	−	5.60106i	0.111842	−	0.193717i
$837$		0			0
$838$	−30.1778	+	17.4232i	−1.04248	+	0.601873i
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	−0.897331	−	0.441359i	$-0.854496\pi$
$839$	−1.92438	+	3.33313i	−0.0664370	+	0.115072i	0.830894	+	0.556431i	$0.187830\pi$
$840$		0			0
$841$	−5.86545	−	10.1593i	−0.202257	−	0.350319i
$842$	−4.92936	−	2.84597i	−0.169877	−	0.0980785i
$843$		0			0
$844$	−5.15561	−	8.92978i	−0.177463	−	0.307376i
$845$	11.7963	+	20.4317i	0.405804	+	0.702873i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		0			0
$850$			0.918875i			0.0315171i
$851$		−	33.8025i		−	1.15874i
$852$		0			0
$853$	26.3470	+	15.2114i	0.902103	+	0.520830i	0.877882	−	0.478877i	$-0.158956\pi$
$853$	26.3470	+	15.2114i	0.902103	+	0.520830i	0.0242213	+	0.999707i	$0.492289\pi$
$854$		0			0
$855$		0			0
$856$	2.35782	+	4.08386i	0.0805885	+	0.139583i
$857$	19.4657	+	33.7156i	0.664937	+	1.15170i	0.979303	+	0.202402i	$0.0648748\pi$
$857$	19.4657	+	33.7156i	0.664937	+	1.15170i	−0.314366	+	0.949302i	$0.601792\pi$
$858$		0			0
$859$	11.5922	+	6.69275i	0.395520	+	0.228354i	0.684549	−	0.728967i	$-0.259999\pi$
$859$	11.5922	+	6.69275i	0.395520	+	0.228354i	−0.289029	+	0.957320i	$0.593332\pi$
$860$	4.13611	+	7.16396i	0.141040	+	0.244289i
$861$		0			0
$862$	15.1468	−	26.2350i	0.515901	−	0.893567i
$863$	−18.8118	+	10.8610i	−0.640360	+	0.369712i	−0.784753	−	0.619809i	$-0.787210\pi$
$863$	−18.8118	+	10.8610i	−0.640360	+	0.369712i	0.144393	+	0.989520i	$0.453877\pi$
$864$		0			0
$865$	−2.33465	+	4.04373i	−0.0793804	+	0.137491i
$866$	−23.6094			−0.802279
$867$		0			0
$868$		0			0
$869$	64.0496	−	36.9791i	2.17273	−	1.25443i
$870$		0			0
$871$	−16.1920	+	9.34845i	−0.548645	+	0.316760i
$872$	−3.66908	−	2.11835i	−0.124251	−	0.0717363i
$873$		0			0
$874$			4.18711i			0.141631i
$875$		0			0
$876$		0			0
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	−0.869318	−	0.494253i	$-0.835442\pi$
$877$	−0.196152	+	0.339746i	−0.00662360	+	0.0114724i	0.862695	+	0.505725i	$0.168775\pi$
$878$	25.0202			0.844392
$879$		0			0
$880$			13.3365i			0.449574i
$881$	43.3363			1.46004			0.730018	−	0.683427i	$-0.239511\pi$
$881$	43.3363			1.46004			0.730018	+	0.683427i	$0.239511\pi$
$882$		0			0
$883$	2.17403			0.0731618			0.0365809	−	0.999331i	$-0.488353\pi$
$883$	2.17403			0.0731618			0.0365809	+	0.999331i	$0.488353\pi$
$884$		−	3.04212i		−	0.102318i
$885$		0			0
$886$	−23.0300			−0.773708
$887$	−5.72215	+	9.91105i	−0.192131	+	0.332781i	−0.945956	−	0.324294i	$-0.894873\pi$
$887$	−5.72215	+	9.91105i	−0.192131	+	0.332781i	0.753825	+	0.657075i	$0.228207\pi$
$888$		0			0
$889$		0			0
$890$		−	2.72774i		−	0.0914341i
$891$		0			0
$892$	−6.24329	−	3.60456i	−0.209041	−	0.120690i
$893$	−11.6526	+	6.72762i	−0.389939	+	0.225131i
$894$		0			0
$895$	−16.9100	+	9.76302i	−0.565240	+	0.326342i
$896$		0			0
$897$		0			0
$898$	15.9028			0.530684
$899$	17.3916	−	30.1232i	0.580043	−	1.00466i
$900$		0			0
$901$		0			0
$902$	−22.6902	+	39.3006i	−0.755501	+	1.30857i
$903$		0			0
$904$	−3.41614	−	5.91693i	−0.113619	−	0.196794i
$905$	31.4430	+	18.1536i	1.04520	+	0.603447i
$906$		0			0
$907$	26.9446	+	46.6694i	0.894680	+	1.54963i	0.834200	+	0.551462i	$0.185930\pi$
$907$	26.9446	+	46.6694i	0.894680	+	1.54963i	0.0604797	+	0.998169i	$0.480737\pi$
$908$	−6.37800	−	11.0470i	−0.211661	−	0.366608i
$909$		0			0
$910$		0			0
$911$	7.00460	+	4.04411i	0.232073	+	0.133987i	0.611528	−	0.791223i	$-0.290555\pi$
$911$	7.00460	+	4.04411i	0.232073	+	0.133987i	−0.379455	+	0.925210i	$0.623889\pi$
$912$		0			0
$913$		−	71.2193i		−	2.35702i
$914$			5.66614i			0.187419i
$915$		0			0
$916$	−3.89208	−	2.24709i	−0.128598	−	0.0742460i
$917$		0			0
$918$		0			0
$919$	−12.8375	−	22.2353i	−0.423472	−	0.733474i	0.572805	−	0.819692i	$-0.305855\pi$
$919$	−12.8375	−	22.2353i	−0.423472	−	0.733474i	−0.996276	+	0.0862175i	$0.972522\pi$
$920$	−4.31705	−	7.47736i	−0.142329	−	0.246521i
$921$		0			0
$922$	27.2438	+	15.7292i	0.897226	+	0.518014i
$923$	3.88777	+	6.73382i	0.127968	+	0.221646i
$924$		0			0
$925$	2.38903	−	4.13792i	0.0785507	−	0.136054i
$926$	7.88340	−	4.55148i	0.259064	−	0.149571i
$927$		0			0
$928$	−2.07781	+	3.59886i	−0.0682073	+	0.118139i
$929$	−10.8524			−0.356055			−0.178027	−	0.984026i	$-0.556972\pi$
$929$	−10.8524			−0.356055			−0.178027	+	0.984026i	$0.556972\pi$
$930$		0			0
$931$		0			0
$932$	−1.86545	+	1.07702i	−0.0611048	+	0.0352789i
$933$		0			0
$934$	26.2433	−	15.1516i	0.858708	−	0.495775i
$935$	20.4296	+	11.7950i	0.668118	+	0.385738i
$936$		0			0
$937$			0.458120i			0.0149661i	0.999972	+	0.00748306i	$0.00238195\pi$
$937$			0.458120i			0.0149661i	−0.999972	+	0.00748306i	$0.997618\pi$
$938$		0			0
$939$		0			0
$940$	13.8728	−	24.0284i	0.452482	−	0.783721i
$941$	7.37780			0.240510			0.120255	−	0.992743i	$-0.461629\pi$
$941$	7.37780			0.240510			0.120255	+	0.992743i	$0.461629\pi$
$942$		0			0
$943$		−	29.3794i		−	0.956725i
$944$	−2.22966			−0.0725693
$945$		0			0
$946$	19.9879			0.649862
$947$		−	11.9910i		−	0.389657i	−0.980837	−	0.194828i	$-0.937585\pi$
$947$		−	11.9910i		−	0.389657i	0.980837	−	0.194828i	$-0.0624150\pi$
$948$		0			0
$949$	−9.18802			−0.298256
$950$	−0.295928	+	0.512563i	−0.00960118	+	0.0166297i
$951$		0			0
$952$		0			0
$953$			58.6883i			1.90110i	0.310572	+	0.950550i	$0.399479\pi$
$953$			58.6883i			1.90110i	−0.310572	+	0.950550i	$0.600521\pi$
$954$		0			0
$955$	25.1031	+	14.4933i	0.812317	+	0.468992i
$956$	−8.78317	+	5.07096i	−0.284068	+	0.164007i
$957$		0			0
$958$	−4.03816	+	2.33143i	−0.130467	+	0.0753251i
$959$		0			0
$960$		0			0
$961$	−39.0600			−1.26000
$962$	−7.90935	+	13.6994i	−0.255008	+	0.441686i
$963$		0			0
$964$	−9.13490	+	5.27404i	−0.294215	+	0.169865i
$965$	5.16140	−	8.93981i	0.166151	−	0.287783i
$966$		0			0
$967$	−3.37560	−	5.84671i	−0.108552	−	0.188018i	0.806632	−	0.591054i	$-0.201288\pi$
$967$	−3.37560	−	5.84671i	−0.108552	−	0.188018i	−0.915184	+	0.403037i	$0.867955\pi$
$968$	18.3810	+	10.6123i	0.590789	+	0.341092i
$969$		0			0
$970$	−5.39218	−	9.33953i	−0.173133	−	0.299874i
$971$	3.20362	+	5.54883i	0.102809	+	0.178070i	0.912841	−	0.408315i	$-0.133884\pi$
$971$	3.20362	+	5.54883i	0.102809	+	0.178070i	−0.810032	+	0.586386i	$0.800550\pi$
$972$		0			0
$973$		0			0
$974$	−16.8720	−	9.74105i	−0.540613	−	0.312123i
$975$		0			0
$976$			8.99970i			0.288073i
$977$		−	13.5987i		−	0.435062i	−0.976053	−	0.217531i	$-0.930200\pi$
$977$		−	13.5987i		−	0.435062i	0.976053	−	0.217531i	$-0.0698004\pi$
$978$		0			0
$979$	−5.70793	−	3.29547i	−0.182426	−	0.105324i
$980$		0			0
$981$		0			0
$982$	−10.2443	−	17.7437i	−0.326910	−	0.566224i
$983$	11.3849	+	19.7192i	0.363122	+	0.628946i	0.988473	−	0.151398i	$-0.0483774\pi$
$983$	11.3849	+	19.7192i	0.363122	+	0.628946i	−0.625351	+	0.780344i	$0.715044\pi$
$984$		0			0
$985$	22.1497	+	12.7882i	0.705749	+	0.407464i
$986$	3.67528	+	6.36577i	0.117045	+	0.202728i
$987$		0			0
$988$	0.979729	−	1.69694i	0.0311693	−	0.0539869i
$989$	−11.2066	+	6.47011i	−0.356348	+	0.205738i
$990$		0			0
$991$	13.4953	−	23.3745i	0.428691	−	0.742515i	−0.568066	−	0.822983i	$-0.692308\pi$
$991$	13.4953	−	23.3745i	0.428691	−	0.742515i	0.996757	+	0.0804680i	$0.0256415\pi$
$992$	8.37019			0.265754
$993$		0			0
$994$		0			0
$995$	56.0869	−	32.3818i	1.77807	−	1.02657i
$996$		0			0
$997$	−16.7263	+	9.65694i	−0.529728	+	0.305838i	−0.740906	−	0.671609i	$-0.765603\pi$
$997$	−16.7263	+	9.65694i	−0.529728	+	0.305838i	0.211178	+	0.977448i	$0.432270\pi$
$998$	−8.87845	−	5.12598i	−0.281043	−	0.162260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.l.b.521.3		16
3.2	odd	2		882.2.l.a.227.6		16
7.2	even	3		2646.2.t.a.1979.2		16
7.3	odd	6		378.2.m.a.251.6		16
7.4	even	3		378.2.m.a.251.7		16
7.5	odd	6		2646.2.t.a.1979.3		16
7.6	odd	2	inner	2646.2.l.b.521.2		16
9.4	even	3		882.2.t.b.815.5		16
9.5	odd	6		2646.2.t.a.2285.3		16
21.2	odd	6		882.2.t.b.803.8		16
21.5	even	6		882.2.t.b.803.5		16
21.11	odd	6		126.2.m.a.83.2	yes	16
21.17	even	6		126.2.m.a.83.3	yes	16
21.20	even	2		882.2.l.a.227.7		16
28.3	even	6		3024.2.cc.b.2897.2		16
28.11	odd	6		3024.2.cc.b.2897.7		16
63.4	even	3		126.2.m.a.41.3	yes	16
63.5	even	6	inner	2646.2.l.b.1097.7		16
63.11	odd	6		1134.2.d.a.1133.15		16
63.13	odd	6		882.2.t.b.815.8		16
63.23	odd	6	inner	2646.2.l.b.1097.6		16
63.25	even	3		1134.2.d.a.1133.2		16
63.31	odd	6		126.2.m.a.41.2	✓	16
63.32	odd	6		378.2.m.a.125.6		16
63.38	even	6		1134.2.d.a.1133.10		16
63.40	odd	6		882.2.l.a.509.2		16
63.41	even	6		2646.2.t.a.2285.2		16
63.52	odd	6		1134.2.d.a.1133.7		16
63.58	even	3		882.2.l.a.509.3		16
63.59	even	6		378.2.m.a.125.7		16
84.11	even	6		1008.2.cc.b.209.6		16
84.59	odd	6		1008.2.cc.b.209.3		16
252.31	even	6		1008.2.cc.b.545.6		16
252.59	odd	6		3024.2.cc.b.881.7		16
252.67	odd	6		1008.2.cc.b.545.3		16
252.95	even	6		3024.2.cc.b.881.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.m.a.41.2	✓	16	63.31	odd	6
126.2.m.a.41.3	yes	16	63.4	even	3
126.2.m.a.83.2	yes	16	21.11	odd	6
126.2.m.a.83.3	yes	16	21.17	even	6
378.2.m.a.125.6		16	63.32	odd	6
378.2.m.a.125.7		16	63.59	even	6
378.2.m.a.251.6		16	7.3	odd	6
378.2.m.a.251.7		16	7.4	even	3
882.2.l.a.227.6		16	3.2	odd	2
882.2.l.a.227.7		16	21.20	even	2
882.2.l.a.509.2		16	63.40	odd	6
882.2.l.a.509.3		16	63.58	even	3
882.2.t.b.803.5		16	21.5	even	6
882.2.t.b.803.8		16	21.2	odd	6
882.2.t.b.815.5		16	9.4	even	3
882.2.t.b.815.8		16	63.13	odd	6
1008.2.cc.b.209.3		16	84.59	odd	6
1008.2.cc.b.209.6		16	84.11	even	6
1008.2.cc.b.545.3		16	252.67	odd	6
1008.2.cc.b.545.6		16	252.31	even	6
1134.2.d.a.1133.2		16	63.25	even	3
1134.2.d.a.1133.7		16	63.52	odd	6
1134.2.d.a.1133.10		16	63.38	even	6
1134.2.d.a.1133.15		16	63.11	odd	6
2646.2.l.b.521.2		16	7.6	odd	2	inner
2646.2.l.b.521.3		16	1.1	even	1	trivial
2646.2.l.b.1097.6		16	63.23	odd	6	inner
2646.2.l.b.1097.7		16	63.5	even	6	inner
2646.2.t.a.1979.2		16	7.2	even	3
2646.2.t.a.1979.3		16	7.5	odd	6
2646.2.t.a.2285.2		16	63.41	even	6
2646.2.t.a.2285.3		16	9.5	odd	6
3024.2.cc.b.881.2		16	252.95	even	6
3024.2.cc.b.881.7		16	252.59	odd	6
3024.2.cc.b.2897.2		16	28.3	even	6
3024.2.cc.b.2897.7		16	28.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(1.17468 - 2.03460i) q^{5} +1.00000i q^{8} +(-2.03460 - 1.17468i) q^{10} +(-4.91614 + 2.83834i) q^{11} +(-1.48943 + 0.859925i) q^{13} +1.00000 q^{16} +(0.884414 - 1.53185i) q^{17} +(0.986680 - 0.569660i) q^{19} +(-1.17468 + 2.03460i) q^{20} +(2.83834 + 4.91614i) q^{22} +(-3.18272 - 1.83755i) q^{23} +(-0.259741 - 0.449885i) q^{25} +(0.859925 + 1.48943i) q^{26} +(-3.59886 - 2.07781i) q^{29} +8.37019i q^{31} -1.00000i q^{32} +(-1.53185 - 0.884414i) q^{34} +(4.59886 + 7.96547i) q^{37} +(-0.569660 - 0.986680i) q^{38} +(2.03460 + 1.17468i) q^{40} +(3.99709 + 6.92317i) q^{41} +(1.76053 - 3.04933i) q^{43} +(4.91614 - 2.83834i) q^{44} +(-1.83755 + 3.18272i) q^{46} -11.8099 q^{47} +(-0.449885 + 0.259741i) q^{50} +(1.48943 - 0.859925i) q^{52} +13.3365i q^{55} +(-2.07781 + 3.59886i) q^{58} -2.22966 q^{59} +8.99970i q^{61} +8.37019 q^{62} -1.00000 q^{64} +4.04054i q^{65} +10.8712 q^{67} +(-0.884414 + 1.53185i) q^{68} -4.52106i q^{71} +(4.62660 + 2.67117i) q^{73} +(7.96547 - 4.59886i) q^{74} +(-0.986680 + 0.569660i) q^{76} -13.0284 q^{79} +(1.17468 - 2.03460i) q^{80} +(6.92317 - 3.99709i) q^{82} +(-6.27298 + 10.8651i) q^{83} +(-2.07781 - 3.59886i) q^{85} +(-3.04933 - 1.76053i) q^{86} +(-2.83834 - 4.91614i) q^{88} +(0.580529 + 1.00551i) q^{89} +(3.18272 + 1.83755i) q^{92} +11.8099i q^{94} -2.67667i q^{95} +(3.97536 + 2.29517i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{4}+O(q^{10}) \) 16 * q - 16 * q^4	\( 16 q - 16 q^{4} - 12 q^{11} + 16 q^{16} - 48 q^{23} - 8 q^{25} + 12 q^{29} + 4 q^{37} + 4 q^{43} + 12 q^{44} - 12 q^{46} - 60 q^{50} - 12 q^{58} - 16 q^{64} + 56 q^{67} + 36 q^{74} + 8 q^{79} - 12 q^{85} - 24 q^{86} + 48 q^{92}+O(q^{100}) \) 16 * q - 16 * q^4 - 12 * q^11 + 16 * q^16 - 48 * q^23 - 8 * q^25 + 12 * q^29 + 4 * q^37 + 4 * q^43 + 12 * q^44 - 12 * q^46 - 60 * q^50 - 12 * q^58 - 16 * q^64 + 56 * q^67 + 36 * q^74 + 8 * q^79 - 12 * q^85 - 24 * q^86 + 48 * q^92

Introduction

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